Photosynthesis provides the energy source for essentially all lifes on Earth. The molecular details of photosynthesis are not yet fully elucidated

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2 Photosynthesis provides the energy source for essentially all lifes on Earth The molecular details of photosynthesis are not yet fully elucidated Remarkable efficiency of photosynthesis processes is not trivial

3 Primary Steps of Photosynthesis ~ 100% quantum yield chlorophyll

4 Light harvesting apparatus of purple bacteria AFM of native photosynthetic membranes of purple bacteria LH2 LH1+RC Bahatyrova et al., Nature 430, 1058 (2004)

5 Light-harvesting apparatus of green bacteria Scholes, Nat. Phys. 6, 402 (2010).

6 FMO Antenna Complexes RC-LH1 LH2 C-Phycocyanin PCP Plant PSI PSII dimer

7 Pigment-Protein Complexes Rhodopseudomonas acidophila Strain 7050 K. McLuskey et al.: Biochemistry 40, 8713 (2001).

8 Fenna-Matthews-Olson Complex (FMO) pigment-protein complex Wire connecting the chlorosome antenna to the reaction center Scholes, Nat. Phys. 6, 402 (2010).

9 Photo excitation Photon LUMO HOMO Ground State Excited State

10 Quantum processes in biology photo excitation HOMO LUMO

11 hole and electron (i) hole transfer t h hole transfer (ii) Electron transfer t e c e 2 1 Electron transfer e c 1 1

12 Exciton transfer (iii) Exciton transfer J Exciton transfer e e 1 2

13 Quantum Environment + Main system A H j j j k A j jk Bath system B (based on normal modes analysis) p m Hˆ V c x x j 2 2 ˆ j j j 2 BI j j j j j 2m 2 jk

14 Normal mode analysis for water 2 p H(, ), 2m j p j q j U q j qk j j jk Hamiltonian is numerically diagonalized Eigenvectors & Eigenenergy Hˆ B j 2 2 pj mj j 2m 2 j x 2 j

15 Normal modes analysis O-H Stretching Libration Translation H-O-H Bending

16 The environments are represented by a sum of oscillators Hˆ B j 2 2 pj mj j 2m 2 j x 2 j By computer simulations or experimental means Moritsugu, Kitao & Kidera, PRL 85, 3970 (2000)

17 Reduced hierarchical equations of motion (HEOM) 0 ˆL ˆ ˆ QM 0 1 t ˆ ˆ i ˆ t ˆ ˆ L ˆ ˆ 1 ˆ QM i 2 i 0 1 ˆ ˆ ˆ ˆ ˆ t L ˆ ˆ ˆQM n i 1 in 1 n n n n N A 1 ˆ ˆ ˆ ˆ ˆ N t L ˆ ˆ ˆ QM N N N N N 1 Y. Tanimura & R. Kubo, J. Phys. Soc. Jpn. 58, 101 (1989). A. Ishizaki & Y. Tanimura, J. Phys. Soc. Jpn. 74, 3131 (2005).

18 Fenna-Matthews-Olson Complex (FMO) pigment-protein complex

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20 Fenna-Matthews-Olson Complex (FMO) pigment-protein complex

21 Revealing Energy Flow in FMO of F MO E e 1 e 2, e 4 1 e 3, e 7 e5, e 6 g Brixner et al. Nature 436, 625 (2005).

22 Long-lived quantum beats in FMO (Theory) 77K (b) (a) 6 1 ~ 700 fs ~ 700 fs K (a) (b) 4 3 ~ 350 fs ~ 350 fs Ishizaki & Fleming, (2009).

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24 Light harvesting apparatus of purple bacteria AFM of native photosynthetic membranes of purple bacteria LH2 LH1+RC Bahatyrova et al., Nature 430, 1058 (2004)

25 Light harvesting apparatus of purple bacteria Structure obtained by K. Miki Group in Kyoto U (Nature 2014) Exciton Transfer Electron Transfer

26 Light Harvesting Complex I Exciton Transfer Electron Transfer RC

27 Exciton transfer vs electron transfer (i) exciton transfer (ii) Electron transfer Electron transfer

28 XT + ET LUMO HOMO M 1 * M 2 M 3 M 4 M 5 M i : a molecule

29 XT + ET Exciton transfer LUMO HOMO M 1 M* 2 M 3 M 4 M 5 M i : a molecule [1]A.G.Dijkstra,Y.Tanimura,J.Chem.Phys.142,212423(2015)

30 XT + ET Exciton transfer LUMO HOMO M 1 M 2 M * 3 M 4 M 5 M i : a molecule [1]A.G.Dijkstra,Y.Tanimura,J.Chem.Phys.142,212423(2015)

31 XT + ET Electron transfer LUMO HOMO M 1 M 2 M M 4 M 5 M i : a molecule

32 XT + ET Electron transfer LUMO HOMO M 1 M 2 M M 4 M i : a molecule M 5

33 System Hamiltonian (6 sites) H S = i ε i (XT) ei >< e i + j ε j (CT) cj >< c j + J i,i+1 ( e i >< e i+1 + h. c. ) i +t e e 4 >< c 5 + c 5 >< c 6 + h. c. Model 1 Model 2 Gelzinis, Valkunas, Fuller, Ogilvie, Mukamel, Abramavicius, NJP 2013, 15, Gelzinis, Abramavicius, Ogilvie, Valkunas, JCP 2017, 147,

34 Model 1: without XCET bath (6bath) Bath for XT system Bath for ET system Environment for XCET system Overdamped Brownian or Drude spectral function [1] Brownian spectral function [2] [1]Y.Tanimura,J.Phys.Soc.Jpn.75,082001(2006). [2] M. Tanaka, Y. Tanimura, 132, (2010)

35 Model 1: with XCET bath (7bath) Environment for XT system Environment for ET system Environment for XCET system Overdamped Brownian or Drude spectral function [2] Brownian spectral function [1] [1]Y.Tanimura,J.Phys.Soc.Jpn.75,082001(2006). [2] M. Tanaka, Y. Tanimura, 132, (2010) V 7 = e 3 >< e 4 + e 4 >< e 3

36 Model 1: without XCET bath (6bath) J 34 = Time[ps] 15 Sakamoto and Tanimura, submitted

37 Model 1: with XCET bath (7bath) J 34 = Time[ps] 15 λ XCET = (= J 34) Sakamoto and Tanimura, submitted

38 Model 2: without XCET bath (5-bath) Environment for XT system Environment for ET system Environment for XCET system Overdamped Brownian or Drude spectral function [2] Brownian spectral function [1]

39 Model 2: with XCET bath (6-bath) Environment for XT system Environment for ET system Environment for XCET system Overdamped Brownian or Drude spectral function [2] Brownian spectral function [1] [1]Y.Tanimura,J.Phys.Soc.Jpn.75,082001(2006). V 7 = e 3 >< e 4 + e 4 >< e 3

40 Model 2: without XCET bath (5-bath) J 23 = 0.01 Weak 0 20 Sakamoto and Tanimura, submitted

41 Model 2: without XCET bath (5-bath) J 23 = 0.1 strong 0 20

42 Model 2: with XCET bath (6-bath) J 23 = 0.01 Weak λ XCET = Sakamoto and Tanimura, submitted